Dynamic functional network connectivity analysis in schizophrenia based on a spatiotemporal CPD framework.

Objective.Dynamic functional network connectivity (dFNC), based on data-driven group independent component (IC) analysis, is an important avenue for investigating underlying patterns of certain brain diseases such as schizophrenia. Canonical polyadic decomposition (CPD) of a higher-way dynamic functional connectivity tensor, can offer an innovative spatiotemporal framework to accurately characterize potential dynamic spatial and temporal fluctuations. Since multi-subject dFNC data from sliding-window analysis are also naturally a higher-order tensor, we propose an innovative sparse and low-rank CPD (SLRCPD) for the three-way dFNC tensor to excavate significant dynamic spatiotemporal aberrant changes in schizophrenia.Approach.The proposed SLRCPD approach imposes two constraints. First, the L1regularization on spatial modules is applied to extract sparse but significant dynamic connectivity and avoid overfitting the model. Second, low-rank constraint is added on time-varying weights to enhance the temporal state clustering quality. Shared dynamic spatial modules, group-specific dynamic spatial modules and time-varying weights can be extracted by SLRCPD. The strength of connections within- and between-IC networks and connection contribution are proposed to inspect the spatial modules. K-means clustering and classification are further conducted to explore temporal group difference.Main results.82 subject resting-state functional magnetic resonance imaging (fMRI) dataset and opening Center for Biomedical Research Excellence (COBRE) schizophrenia dataset both containing schizophrenia patients (SZs) and healthy controls (HCs) were utilized in our work. Three typical dFNC patterns between different brain functional regions were obtained. Compared to the spatial modules of HCs, the aberrant connections among auditory network, somatomotor, visual, cognitive control and cerebellar networks in 82 subject dataset and COBRE dataset were detected. Four temporal states reveal significant differences between SZs and HCs for these two datasets. Additionally, the accuracy values for SZs and HCs classification based on time-varying weights are larger than 0.96.Significance.This study significantly excavates spatio-temporal patterns for schizophrenia disease.

Dynamic functional network connectivity based on spatial source phase maps of complex-valued fMRI data: Application to schizophrenia.

BACKGROUND: Dynamic spatial functional network connectivity (dsFNC) has shown advantages in detecting functional alterations impacted by mental disorders using magnitude-only fMRI data. However, complete fMRI data are complex-valued with unique and useful phase information. METHODS: We propose dsFNC of spatial source phase (SSP) maps, derived from complex-valued fMRI data (named SSP-dsFNC), to capture the dynamics elicited by the phase. We compute mutual information for connectivity quantification, employ statistical analysis and Markov chains to assess dynamics, ultimately classifying schizophrenia patients (SZs) and healthy controls (HCs) based on connectivity variance and Markov chain state transitions across windows. RESULTS: SSP-dsFNC yielded greater dynamics and more significant HC-SZ differences, due to the use of complete brain information from complex-valued fMRI data. COMPARISON WITH EXISTING METHODS: Compared with magnitude-dsFNC, SSP-dsFNC detected additional and meaningful connections across windows (e.g., for right frontal parietal) and achieved 14.6% higher accuracy for classifying HCs and SZs. CONCLUSIONS: This work provides new evidence about how SSP-dsFNC could be impacted by schizophrenia, and this information could be used to identify potential imaging biomarkers for psychotic diagnosis.

Constrained CPD of Complex-Valued Multi-Subject fMRI Data via Alternating Rank-R and Rank-1 Least Squares.

Complex-valued shift-invariant canonical polyadic decomposition (CPD) under a spatial phase sparsity constraint (pcsCPD) shows excellent separation performance when applied to band-pass filtered complex-valued multi-subject fMRI data. However, some useful information may also be eliminated when using a band-pass filter to suppress unwanted noise. As such, we propose an alternating rank- R and rank-1 least squares optimization to relax the CPD model. Based upon this optimization method, we present a novel constrained CPD algorithm with temporal shift-invariance and spatial sparsity and orthonormality constraints. More specifically, four steps are conducted until convergence for each iteration of the proposed algorithm: 1) use rank- R least-squares fit under spatial phase sparsity constraint to update shared spatial maps after phase de-ambiguity; 2) use orthonormality constraint to minimize the cross-talk between shared spatial maps; 3) update the aggregating mixing matrix using rank- R least-squares fit; 4) utilize shift-invariant rank-1 least-squares on a series of rank-1 matrices reconstructed by each column of the aggregating mixing matrix to update shared time courses, and subject-specific time delays and intensities. The experimental results of simulated and actual complex-valued fMRI data show that the proposed algorithm improves the estimates for task-related sensorimotor and auditory networks, compared to pcsCPD and tensorial spatial ICA. The proposed alternating rank- R and rank-1 least squares optimization is also flexible to improve CPD-related algorithm using alternating least squares.

Low-Rank Tucker-2 Model for Multi-Subject fMRI Data Decomposition With Spatial Sparsity Constraint.

Tucker decomposition can provide an intuitive summary to understand brain function by decomposing multi-subject fMRI data into a core tensor and multiple factor matrices, and was mostly used to extract functional connectivity patterns across time/subjects using orthogonality constraints. However, these algorithms are unsuitable for extracting common spatial and temporal patterns across subjects due to distinct characteristics such as high-level noise. Motivated by a successful application of Tucker decomposition to image denoising and the intrinsic sparsity of spatial activations in fMRI, we propose a low-rank Tucker-2 model with spatial sparsity constraint to analyze multi-subject fMRI data. More precisely, we propose to impose a sparsity constraint on spatial maps by using an lp norm ( ), in addition to adding low-rank constraints on factor matrices via the Frobenius norm. We solve the constrained Tucker-2 model using alternating direction method of multipliers, and propose to update both sparsity and low-rank constrained spatial maps using half quadratic splitting. Moreover, we extract new spatial and temporal features in addition to subject-specific intensities from the core tensor, and use these features to classify multiple subjects. The results from both simulated and experimental fMRI data verify the improvement of the proposed method, compared with four related algorithms including robust Kronecker component analysis, Tucker decomposition with orthogonality constraints, canonical polyadic decomposition, and block term decomposition in extracting common spatial and temporal components across subjects. The spatial and temporal features extracted from the core tensor show promise for characterizing subjects within the same group of patients or healthy controls as well.

Siamese anchor-free object tracking with multiscale spatial attentions.

Recently, object trackers based on Siamese networks have attracted considerable attentions due to their remarkable tracking performance and widespread application. Especially, the anchor-based methods exploit the region proposal subnetwork to get accurate prediction of a target and make great performance improvement. However, those trackers cannot capture the spatial information very well and the pre-defined anchors will hinder robustness. To solve these problems, we propose a Siamese-based anchor-free object tracking algorithm with multiscale spatial attentions in this paper. Firstly, we take ResNet-50 as the backbone network to generate multiscale features of both template patch and search regions. Secondly, we propose the spatial attention extraction (SAE) block to capture the spatial information among all positions in the template and search region feature maps. Thirdly, we put these features into the SAE block to get the multiscale spatial attentions. Finally, an anchor-free classification and regression subnetwork is used for predicting the location of the target. Unlike anchor-based methods, our tracker directly predicts the target position without predefined parameters. Extensive experiments with state-of-the-art trackers are carried out on four challenging visual object tracking benchmarks: OTB100, UAV123, VOT2016 and GOT-10k. Those experimental results confirm the effectiveness of our proposed tracker.

Sparse representation of complex-valued fMRI data based on spatiotemporal concatenation of real and imaginary parts.

BACKGROUND: Spatial sparsity has been found to be in line with the intrinsic characteristic of brain activation. However, identifying a sparse representation of complex-valued fMRI data is challenging due to high noise within the phase data. NEW METHODS: We propose to reduce the noise by combining real and imaginary parts of complex-valued fMRI data along spatial and temporal dimensions to form a real-valued spatiotemporal concatenation model. This model not only enables flexible usage of existing real-valued sparse representation algorithms but also allows for the reconstruction of complex-valued spatial and temporal components from their real and imaginary estimates. We propose to select components from both real and imaginary estimates to reconstruct the complex-valued component, using phase denoising to recover weak brain activity from high-amplitude noise. RESULTS: The K-SVD algorithm was used to obtain a sparse representation within the spatiotemporal concatenation model. The results from simulated and experimental complex-valued fMRI datasets validated the efficacy of our method. COMPARISON WITH EXISTING METHODS: Compared to a magnitude-only approach, the proposed method detected additional voxels manifest within several specific regions expected to be involved but likely missing from the magnitude-only data, e.g., in the anterior cingulate cortex region. Simulation results showed that the additional voxels were accurate and unique information from the phase data. Compared to a complex-valued dictionary learning algorithm, our method exhibited lower noise for both magnitude and phase maps. CONCLUSIONS: The proposed method is robust to noise and effective for identifying a sparse representation of the natively complex-valued fMRI data.

Shift-Invariant Canonical Polyadic Decomposition of Complex-Valued Multi-Subject fMRI Data With a Phase Sparsity Constraint.

Canonical polyadic decomposition (CPD) of multi-subject complex-valued fMRI data can be used to provide spatially and temporally shared components among groups with both magnitude and phase information. However, the CPD model is not well formulated due to the large subject variability in the spatial and temporal modalities, as well as the high noise level in complex-valued fMRI data. Considering that the shift-invariant CPD can model temporal variability across subjects, we propose to further impose a phase sparsity constraint on the shared spatial maps to denoise the complex-valued components and to model the inter-subject spatial variability as well. More precisely, subject-specific time delays are first estimated for the complex-valued shared time courses in the framework of real-valued shift-invariant CPD. Source phase sparsity is then imposed on the complex-valued shared spatial maps. A smoothed l0 norm is specifically used to reduce voxels with large phase values after phase de-ambiguity based on the small phase characteristic of BOLD-related voxels. The results from both the simulated and experimental fMRI data demonstrate improvements of the proposed method over three complex-valued algorithms, namely, tensor-based spatial ICA, shift-invariant CPD and CPD without spatiotemporal constraints. When comparing with a real-valued algorithm combining shift-invariant CPD and ICA, the proposed method detects 178.7% more contiguous task-related activations.

Spatial source phase: A new feature for identifying spatial differences based on complex-valued resting-state fMRI data.

Spatial source phase, the phase information of spatial maps extracted from functional magnetic resonance imaging (fMRI) data by data-driven methods such as independent component analysis (ICA), has rarely been studied. While the observed phase has been shown to convey unique brain information, the role of spatial source phase in representing the intrinsic activity of the brain is yet not clear. This study explores the spatial source phase for identifying spatial differences between patients with schizophrenia (SZs) and healthy controls (HCs) using complex-valued resting-state fMRI data from 82 individuals. ICA is first applied to preprocess fMRI data, and post-ICA phase de-ambiguity and denoising are then performed. The ability of spatial source phase to characterize spatial differences is examined by the homogeneity of variance test (voxel-wise F-test) with false discovery rate correction. Resampling techniques are performed to ensure that the observations are significant and reliable. We focus on two components of interest widely used in analyzing SZs, including the default mode network (DMN) and auditory cortex. Results show that the spatial source phase exhibits more significant variance changes and higher sensitivity to the spatial differences between SZs and HCs in the anterior areas of DMN and the left auditory cortex, compared to the magnitude of spatial activations. Our findings show that the spatial source phase can potentially serve as a new brain imaging biomarker and provide a novel perspective on differences in SZs compared to HCs, consistent with but extending previous work showing increased variability in patient data.

Model order effects on ICA of resting-state complex-valued fMRI data: Application to schizophrenia.

BACKGROUND: Component splitting at higher model orders is a widely accepted finding for independent component analysis (ICA) of functional magnetic resonance imaging (fMRI) data. However, our recent study found that intact components occurred with subcomponents at higher model orders. NEW METHOD: This study investigated model order effects on ICA of resting-state complex-valued fMRI data from 82 subjects, which included 40 healthy controls (HCs) and 42 schizophrenia patients. In addition, we explored underlying causes for distinct component splitting between complex-valued data and magnitude-only data by examining model order effects on ICA of phase fMRI data. A best run selection method was proposed to combine subject averaging and a one-sample t-test. We selected the default mode network (DMN)-, visual-, and sensorimotor-related components from the best run of ICA at varying model orders from 10 to 140. RESULTS: Results show that component integration occurred in complex-valued and phase analyses, whereas component splitting emerged in magnitude-only analysis with increasing model order. Incorporation of phase data appears to play a complementary role in preserving integrity of brain networks. COMPARISON WITH EXISTING METHOD(S): When compared with magnitude-only analysis, the intact DMN component obtained in complex-valued analysis at higher model orders exhibited highly significant subject-level differences between HCs and patients with schizophrenia. We detected significantly higher activity and variation in anterior areas for HCs and in posterior areas for patients with schizophrenia. CONCLUSIONS: These results demonstrate the potential of complex-valued fMRI data to contribute generally and specifically to brain network analysis in identification of schizophrenia-related changes.

Adaptive independent vector analysis for multi-subject complex-valued fMRI data.

BACKGROUND: Complex-valued fMRI data can provide additional insights beyond magnitude-only data. However, independent vector analysis (IVA), which has exhibited great potential for group analysis of magnitude-only fMRI data, has rarely been applied to complex-valued fMRI data. The main challenges in this application include the extremely noisy nature and large variability of the source component vector (SCV) distribution. NEW METHOD: To address these challenges, we propose an adaptive fixed-point IVA algorithm for analyzing multiple-subject complex-valued fMRI data. We exploited a multivariate generalized Gaussian distribution (MGGD)- based nonlinear function to match varying SCV distributions in which the MGGD shape parameter was estimated using maximum likelihood estimation. To achieve our de-noising goal, we updated the MGGD-based nonlinearity in the dominant SCV subspace, and employed a post-IVA de-noising strategy based on phase information in the IVA estimates. We also incorporated the pseudo-covariance matrix of fMRI data into the algorithm to emphasize the noncircularity of complex-valued fMRI sources. RESULTS: Results from simulated and experimental fMRI data demonstrated the efficacy of our method. COMPARISON WITH EXISTING METHOD(S): Our approach exhibited significant improvements over typical complex-valued IVA algorithms, especially during higher noise levels and larger spatial and temporal changes. As expected, the proposed complex-valued IVA algorithm detected more contiguous and reasonable activations than the magnitude-only method for task-related (393%) and default mode (301%) spatial maps. CONCLUSIONS: The proposed approach is suitable for decomposing multi-subject complex-valued fMRI data, and has great potential for capturing additional subject variability.

Multi-subject fMRI analysis via combined independent component analysis and shift-invariant canonical polyadic decomposition.

BACKGROUND: Canonical polyadic decomposition (CPD) may face a local optimal problem when analyzing multi-subject fMRI data with inter-subject variability. Beckmann and Smith proposed a tensor PICA approach that incorporated an independence constraint to the spatial modality by combining CPD with ICA, and alleviated the problem of inter-subject spatial map (SM) variability. NEW METHOD: This study extends tensor PICA to incorporate additional inter-subject time course (TC) variability and to connect CPD and ICA in a new way. Assuming multiple subjects share common TCs but with different time delays, we accommodate subject-dependent TC delays into the CP model based on the idea of shift-invariant CP (SCP). We use ICA as an initialization step to provide the aggregating mixing matrix for shift-invariant CPD to estimate shared TCs with subject-dependent delays and intensities. We then estimate shared SMs using a least-squares fit post shift-invariant CPD. RESULTS: Using simulated fMRI data as well as actual fMRI data we demonstrate that the proposed approach improves the estimates of the shared SMs and TCs, and the subject-dependent TC delays and intensities. The default mode component illustrates larger TC delays than the task-related component. COMPARISON WITH EXISTING METHOD(S): The proposed approach shows improvements over tensor PICA in particular when TC delays are large, and also outperforms SCP with SM orthogonality constraint and SCP with ICA-based SM initialization. CONCLUSIONS: TCs with subject-dependent delays conform to the true situation of multi-subject fMRI data. The proposed approach is suitable for decomposing multi-subject fMRI data with large inter-subject temporal and spatial variability.

ICA of full complex-valued fMRI data using phase information of spatial maps.

BACKGROUND: ICA of complex-valued fMRI data is challenging because of the ambiguous and noisy nature of the phase. A typical solution is to remove noisy regions from fMRI data prior to ICA. However, it may be more optimal to carry out ICA of full complex-valued fMRI data, since any filtering or voxel-based processing may disrupt information that can be useful to ICA. NEW METHOD: We enable ICA of the full complex-valued fMRI data by utilizing phase information of estimated spatial maps (SMs). The SM phases are first adjusted to properly represent spatial phase changes of all voxels based on estimated time courses (TCs), and then these are used to segment the voxels into BOLD-related and unwanted voxels based on a criterion of TC real-part power maximization. Single-subject and group phase masks are finally constructed to remove the unwanted voxels from the individual and group SM estimates. RESULTS: Our method efficiently estimated not only the task-related component but also the non-task-related component DMN. COMPARISON WITH EXISTING METHOD(S): Our method extracted 139-331% more contiguous and reasonable activations than magnitude-only infomax for the task-related component and DMN at |Z|>2.5, and detected more BOLD-related voxels, but eliminated more unwanted voxels than ICA of complex-valued fMRI data with pre-ICA de-noising. Our TC-based phase de-ambiguity exhibited higher accuracy and robustness than the SM-based method. CONCLUSIONS: The TC-based phase de-ambiguity is essential to prepare the SM phases. The SM phases provide a new post-ICA index for reliably identifying and suppressing the unwanted voxels.

Tensor decomposition of EEG signals: a brief review.

Electroencephalography (EEG) is one fundamental tool for functional brain imaging. EEG signals tend to be represented by a vector or a matrix to facilitate data processing and analysis with generally understood methodologies like time-series analysis, spectral analysis and matrix decomposition. Indeed, EEG signals are often naturally born with more than two modes of time and space, and they can be denoted by a multi-way array called as tensor. This review summarizes the current progress of tensor decomposition of EEG signals with three aspects. The first is about the existing modes and tensors of EEG signals. Second, two fundamental tensor decomposition models, canonical polyadic decomposition (CPD, it is also called parallel factor analysis-PARAFAC) and Tucker decomposition, are introduced and compared. Moreover, the applications of the two models for EEG signals are addressed. Particularly, the determination of the number of components for each mode is discussed. Finally, the N-way partial least square and higher-order partial least square are described for a potential trend to process and analyze brain signals of two modalities simultaneously.